Chapter 8.2, Problem 44E

To determine

To sketch the graph of the given polar equation -

  $r=sin\left(8\theta /5\right)$

Answer to Problem 44E

The graph of polar equation is

  

Explanation of Solution

Given: Polar equation: $r=sin\left(8\theta /5\right)$

Formula Used:

A polar equation is any equation that describes a relation between r and θ , where r represents the distance from the pole (origin) to a point on a curve, and θ represents the counter-clockwise angle made by a point on a curve, the pole, and the positive x-axis.

Also, $x=r\cos \theta$ and $y=r\sin \theta$

  $r=\sqrt{x^2+y^2}$ and $\theta ={\tan }^{-1}\left(\frac{y}{x}\right)$

Calculation:

Given Polar equation is $r=sin\left(8\theta /5\right)$

Drawing the polar-form curve for $r=sin\left(8\theta /5\right)$ on a graph as per the above definition of polar equation, we have:

Plotting the above points on the graph using the graphing device, we have:

  

Conclusion:

Hence, the graph of polar equation is